Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 705 · Overbeck, fol. 12r

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.96.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 13v); this page is its right half.

The machine reads it as

  1. Exponetes
  2. Amplissina, Consultissime atque Excellentissime
  3. omine Consiliarie Intime Electoralis Gravrssine
  4. Somine Maecenas e Patrone aeternâ Observantia
  5. Suspiciende
  6. Cum proximâ occasione Tuam Excellentiam salutatum admitterer inter
  7. alia sermo fuit de Theoremate Numerorum primorum (Z = - 1): y - in
  8. Utrum illud ad Praxin utile sit nec ne, a tua Excell(. jussus sum inquirere
  9. Integru Theorema requirit, seriem Numerorum pariter parium con
  10. finuari usque ad Exponentem y-1. et Numeru ibi acceptum dividi
  11. per y. Quod si ibi Residuum Divisionis fuerit Unitas ipsum
  12. y. fore Numerion primum, e contra. Hic integros pariter
  13. pares retinere non licebat, cum facile y. tam magnum sumatur
  14. ut pariter parem tanti exponentis oir sine errore iniquo la
  15. bore exhibere liceat. Sed rem recte examinando vidi non in
  16. tegrum pariter parem Exponetis y. requiri, sed saltem ejus
  17. residutem, abjecto y. quoties licet. Suscepi rgitur Calculuque
  18. talium Residuorum sub usdem Exponentibus sub quibus eorum
  19. integri pariter pares locantur, d vidi haec Residua non minus Loga
  20. rithmice tractari posse, quam eorum Numeros integros scilicet ut Pro
  21. ductum duorum Residuorum (abjectoy quoties licet) fiat Residuum
  22. sub summa Exponentium, aut Quadratum Residui sub Duplo Ex
  23. ponente. Exemeligr. si sit y = 109 ponatur haec series
  24. 0. 1. 2. 3. 4. 5. 6. 7.
  25. Pariter pares 1. 2. 4. 9. 16. 37. 64. 128
  26. 8. 9. 10
  27. 11. 12.
  28. 13.
  29. 14. 15 16. 17. 18
  30. Residua ablato (109) ubi licet, . - - 19. 38. 76. 152 = 43. 86, 172 -63 126 = 17, 34. 68. 136 -27, 54. 108-:
  31. Quia jam sub Exponente 18, est Residuum = 1, sub Daplo Exponete (36) erit
  32. Qvadratum ex - 1, nepe +1, et sub triplo Exponente (54) erit (ubus
  33. ejus iterum - 1. Et sub hujus duplo (108) erit Quadratu ex hoc
  34. Cubo :1, id est iterum +1. Sed 108 =y -1, Ergo sub Exponente
  35. y. 1 accipio Residuum +1. Ergo per LElBXISI A N A, ipsum
  36. 109 erit Numerus primus.
  37. Aliter (7) 19. id est Exponens 7. dat Residuu 19. Hujus Quadratum 361.
  38. abjecto ter 109 dat Residuum 34. Ergo (14) 34 e multiplicando per
  39. 16. Residuu Exponetis (4) prodit (18)544, e abjecto quinquies 109
  40. prodit (18) - 1. Ergo (54) -1, _ (108) +1. Ergo 9 109 est Num. prme
  41. Numerus in Parethesi notat Exponentem, et qui ei apponitur notat ipsie Residiu

Cite

LBr. 705 · Overbeck, fol. 12r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-861255:0023?run=74